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Optimal impulsive control of delay systems

Published online by Cambridge University Press:  30 January 2008

Florent Delmotte ,
Erik I. Verriest  and
Magnus Egerstedt
Florent Delmotte
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
Erik I. Verriest
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
Magnus Egerstedt
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30302, USA; florent@ece.gatech.edu; erik.verriest@ece.gatech.edu; magnus@ece.gatech.edu
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Abstract

In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation. A locally optimal impulsive control strategy can then be found using a numerical gradient descent algorithm.

Keywords

Optimal controlimpulse controlswitched systemsdelay systemscalculus of variation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 767 - 779
Copyright
© EDP Sciences, SMAI, 2008

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